English

Fourier Eigenfunctions, Uncertainty Gabor Principle and Isoresolution Wavelets

Classical Analysis and ODEs 2015-02-18 v3

Abstract

Shape-invariant signals under Fourier transform are investigated leading to a class of eigenfunctions for the Fourier operator. The classical uncertainty Gabor-Heisenberg principle is revisited and the concept of isoresolution in joint time-frequency analysis is introduced. It is shown that any Fourier eigenfunction achieve isoresolution. It is shown that an isoresolution wavelet can be derived from each known wavelet family by a suitable scaling.

Keywords

Cite

@article{arxiv.1502.03401,
  title  = {Fourier Eigenfunctions, Uncertainty Gabor Principle and Isoresolution Wavelets},
  author = {L. R. Soares and H. M. de Oliveira and R. J. Cintra and R. M. Campello de Souza},
  journal= {arXiv preprint arXiv:1502.03401},
  year   = {2015}
}

Comments

6 pages, XX Simp\'osio Bras. de Telecomunica\c{c}\~oes, Rio de Janeiro, Brazil, 2003. Fixed typos

R2 v1 2026-06-22T08:27:50.519Z